Does {$f_n$} defined by $f_n= n 1_{(1/n , 1]}$ converge to $0$ pointwise?. Clearly $\int f_n \rightarrow \infty$ as $n \rightarrow \infty$.
2026-02-24 00:49:28.1771894168
Convergence of the sequence defined by $f_n=n1_{(1/n ,1]}$
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No it doesn't since $f_n(1)=n$.